Joints in Steel construction

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Structural Steelwork Eurocodes

Development of

A Trans-national Approach

Course: Eurocode 3

Module 5 : Structural joints

Lecture 15 : Generalities about structural joints

Summary:

Traditionally structural joints are considered as rigidorpinned.

An intermediate behaviour may be considered: joints are then said semi-rigid.

The concept of semi-rigidity is introduced.

The merits of this concept are discussed.

Aparallel between member sections and jointsin the semi-rigid approach is then established.

In a structural frame, four types of joint configurations have to be distinguished: beam-to column joints,beam splices, column splices and column bases

The wordsjointsand connectionshave to be clearly differentiated.

For each type of joint configuration, the possible sources of deformabilityare specified.

Stiffness, strength and ductility classesof structural joints are introduced.

The process of joint modellingfor structural frame analysis is described.

Pre-requisites:

Basic knowledge about frame analysis and design.

Notes for Tutors:

This material comprises one 90 minutes lecture.

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Structural Steelwork Eurocodes Development of a Trans-National Approach

Structural joints

Generalities about structural joints

Objectives:

The student should:

Know that joints may be considered as pinned, semi-rigid or rigid.

Know how to profit from the new semi-rigid concept Understand physically how structural joints behave and deform.

Be able to classify joints

Be able to select the appropriate joint model for frame analysis

References:

Revised Annex J of Eurocode 3, "Joints in Building Frames", Amendment 2 to ENV 1993-1-1, 1998

Frame design including joint behaviour. Users manual published by the European Union, Report EUR

18563 EN, Office for Official Publications, Luxembourg, 1998 (ISBN 92-828-4904-X)

Contents

1. A consistent approach for structural joints

2. The merits of the consistent approach for structural joints

3. A parallel between member sections and joints

4. Definitions of joint configuration, joint and connection

5. Sources of joint deformability

5.1. Beam-to-column joints

5.2. Beam splices and column splices

5.3. Beam-to-beam joints

5.4. Column bases

6. Joint classification

6.1. General

6.2. Stiffness classification

6.3. Strength classification

6.4. Boundaries for classification

6.5. Ductility classes

7. Joint modelling

7.1. General

7.2. Modelling and sources of joint deformability

7.3. Simplified modelling according to Eurocode 3

7.4. Concentration of the joint deformability

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1. A consistent approach for structural jointsThe rotational behaviour of actual joints is well recognised as being often intermediate between

the two extreme situations, i.e. rigid or pinned.Later in this lecture, the difference betweenjointsand connectionswill be introduced. For the

time being, examples of joints between one beam and one column only will be used.

Consider now the bending moments and the related rotations at a joint (Figure 1):

(a) Rigid joint (b) Pinned joint (c) Semi-rigid joint

Figure 1 Classification of joints according to stif fness

When all the different parts in the joint are sufficiently stiff (i.e. ideally infinitely stiff), the joint

is rigid, and there is no difference between the respective rotations at the ends of the members

connected at this joint (Figure 1.a). The joint experiences a single global rigid-body rotation

which is the nodal rotation in the commonly used analysis methods for framed structures.

Should the joint be without any stiffness, then the beam will behave just as simply supportedwhatever the behaviour of the other connected member(s) (Figure 1.b). This is apinnedjoint.

For intermediate cases (non zero and non infinite stiffness), the transmitted moment will result

in there being a difference between the absolute rotations of the two connected members

(Figure 1.c). The joint is semi-rigid in these cases.

The simplest means for representing the concept is a rotational (spiral) spring between the ends

of the two connected members. The rotational stiffness S of this spring is the parameter that

links the transmitted momentMj to the relative rotation ,which is the difference between the

absolute rotations of the two connected members.

When this rotational stiffness Sis zero, or when it is relatively small, the joint falls back into the

pinned joint class. In contrast, when the rotational stiffness Sis infinite, or when it is relatively

high, the joint falls into the rigid joint class. In all the intermediate cases, the joint belongs to the

semi-rigid joint class.

For semi-rigid joints the loads will result in both a bending momentMjand a relative rotation

between the connected members. The moment and the relative rotation are related through a

constitutive law which depends on the joint properties. This is illustrated in Figure 2, where, for

the sake of simplicity, the global analysis is assumed to be performed with linear elastic

assumptions.

At the global analysis stage, the effect of having semi-rigid joints instead of rigid or pinned

joints is to modify not only the displacements, but also the distribution and magnitude of the

internal forces throughout the structure.

As an example, the bending moment diagrams in a fixed-base simple portal frame subjected to a

uniformly distributed load are given in Figure 3 for two situations, where the beam-to-column

joints are respectively either pinned or semi-rigid. The same kind of consideration holds for

deflections.

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Mj

MjMj

(a) Rigid joint (b) Pinned joint (c) Semi-rigid joint

(= 0) (Mj = 0) (Mj and 0)

Figure 2 Modelling of joints (case of elastic global analysis)

(a) Pinned joints (b) Semi-rigid joints

Figure 3 Elastic distribution of bending moments in a simple portal

frame

2. The merits of the consistent approach for structural

jointsBoth the Eurocode 3requirements and the desire to model the behaviour of the structure in a

more realistic way leads to the consideration of the semi-rigid behaviour when necessary.

Many designers would stop at that basic interpretation of Eurocode 3 and hence would be

reluctant to confront the implied additional computational effort involved. Obviously a crude

way to deal with this new burden will be for them to design joints that will actually continue to

be classified as being either pinned or fully rigid. However such properties will have to be

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proven at the end of the design process and, in addition, such joints will certainly be found to be

uneconomical in a number of situations.

It should be noted that the concept of rigid and pinned joints still exists in Eurocode 3. It is

accepted that a joint which is almost rigid, or almost pinned,may still be considered as being

truly rigidor truly pinnedin the design process. How to judge whether a joint can be considered

as rigid, semi-rigid or pinned depends on the comparison between the joint stiffness and the

beam stiffness, which depends on the second moment of area and length of the beam.

The designer is strongly encouraged to go beyond this "all or nothing" attitude. Actually it is

important to consider the benefits to be gained from the semi-rigid behaviour of joints. Those

benefits can be brought in two ways :

1. The designer decides to continue with the practice of assuming -sometimes erroneously- thatjoints are either pinned or fully rigid. However, Eurocode 3 requires that proper

consideration be given to the influence that the actual behaviour of the joints has on the

global behaviour of the structure, i.e. on the precision with which the distribution of forces

and moments and the displacements have been determined. This may not prove to be easy

when the joints are designed at a late stage in the design process since some iterations

between global analysis and design checking may be required. Nevertheless, the followingsituations can be foreseen:

So that a joint can be assumed to be rigid, it is common practice to introduce webstiffeners in the column. Eurocode 3now provides the means to check whether

such stiffeners are really necessary for the joint to be both rigid and have

sufficient resistance. There are practical cases where they are not needed, thus

permitting the adoption of a more economical joint design.

When joints assumed to be pinned are later found to have fairly significantstiffness (i.e. to be semi-rigid), the designer may be in a position to reduce beam

sizes. This is simply because the moments carried by the joints reduce the span

moments in the beams.

2. The designer decides to give consideration, at the preliminary design stage, not only to the

properties of the members but also to those of the joints. It may be shown that this new

approach is not at all incompatible with the sometimes customary separation of the designtasks between those who have the responsibility for conceiving the structure and carrying

out the global analysis and those who have the responsibility for designing the joints.

Indeed, both tasks are very often performed by different people, or indeed, by different

companies, depending on national or local industrial habits. Adopting this novel early

consideration of joints in the design process requires a good understanding of the balance

between, on the one hand, the costs and the complexity of joints and, on the other hand, the

optimisation of the structural behaviour and performance through the more accurate

consideration of joint behaviour for the design as a whole. Two examples are given to

illustrate this:

It was mentioned previously that it is possible in some situations to eliminatecolumn web stiffeners and therefore to reduce costs. Despite the reduction in its

stiffness and, possibly, in its strength, the joint can still be considered to be rigidand be found to have sufficient strength. This is shown to be possible for

industrial portal frames with rafter-to-column haunch joints, in particular, but

other cases can be envisaged.

In a more general way, it is worthwhile to consider the effect of adjusting the jointstiffness so as to strike the best balance between the cost of the joints and the

costs of the beams and the columns. For instance, for braced frames, the use of

semi-rigid joints, which are probably more costly than the pinned joints, leads to

reducing the beam sizes. For unbraced frames, the use of less costly semi-rigid

joints, instead of the rigid joints, leads to increased beam sizes and possibly

column sizes.

Of course the task may seem a difficult one, and this is why the present lectures are aimed at

providing the reader with useful information. The whole philosophy could be termed as

"Because you must do it, take advantage of it".Thus Eurocode 3 now presents the designer with a choice between a traditionalist attitude,

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where however something may often be gained, and an innovative attitude, where the most

economical result may best be sought.

It is important to stress the high level of similarity that exists between the member classification

and the joint classification. This topic is addressed in the next section.

3. A parallel between member sections and jointsMember cross-section behaviour may be considered through an M- curve for a simply

supported beam loaded at mid span (M : bending-moment at mid-span ; :sum of rotations at

the span ends). Joint behaviour will be considered through a similar relationship, but with M =

Mjbeing the bending moment transmitted by the joint and being the relative rotation between

the connected member and the rest of the joint. Those relationships have similar shapes as

illustrated in Figure 4.

To flexural stiffnessEI/Land the design resistance Mb.Rdof the member correspond the initial

stiffness Sj,iniand the design resistanceMj.Rdof the joint.

According toEurocode 3member cross-sections are divided into four classes according to their

varying ability to resist local instability, when partially or totally subject to compression, and

the consequences this may have on the possibility for plastic redistribution. Therefore their

resistance ranges from the full plastic resistance (class 1and 2) to the elastic resistance (class3)

or a reduced elastic resistance (class4) as explained in the Lecture on "Local buckling and

section classification".

/2/2

Joint

Mj,RdMb.Rd

Member

EI/L Sj,ini

Figure 4 M- characteristics for member cross-section and jointThe allocation of a cross-section to a specific class is governed by the assumptions on:

The behaviour to be idealised for global analysis (i.e. class 1will allow the formation of aplastic hinge and permit the redistribution of internal forces in the frame as loads are

increased up to or beyond the design loads);

The behaviour to be taken into account for local design checks (i.e. class 4will imply that

the resistance of the cross-section is based on the properties of a relevant effective cross-

section rather than of the gross cross-section).

In Eurocode 3, the classification of a cross-section is based on the width-to-thickness ratio of

the component walls of the section. Ductility is directly related to the amount of rotation during

which the design bending resistance will be sustained. For joints, the rotation capacityconcept

is equivalent to the ductility concept for sections.

In a manner similar to that for member cross-sections, joints are classified in terms of ductility

or rotation capacity. This classification is a measure of their ability to resist premature localinstability and, even more likely, premature brittle failure (especially due to bolt failure) with

due consequences on the type of global analysis allowed.

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The practical interest of such a classification for joints is to check whether an elasto-plastic

global analysis may be conducted up to the formation of a plastic collapse mechanism in the

structure, which implies such hinges in at least some of the joints.

Mj

Figure 5 Ductility or rotation capacity in joints

As will be shown, this classification of joints by ductility, while not explicitly stated in

Eurocode 3, may be defined from the geometric and mechanical properties of the joint

components (bolts, welds, plate thickness, etc.).

Joints may therefore be classified according to both their stiffnessand their ductility. Moreover,

joints may be classified according to their strength.

In terms of their strength, joints are classified as full-strengthor partial-strengthaccording to

their resistance compared to the resistance of the connected members. For elastic design, the use

of partial-strength joints is well understood. When plastic design is used, the main use of this

classification is to foresee the possible need to allow a plastic hinge to form in the joint during

the global analysis. In order to permit a further increase of loads beyond that corresponding to

the formation of the hinge, a partial-strength joint may be required to act as a hinge from the

moment when its plastic bending resistance is reached. In that case, the joint must also havesufficient ductility.

4. Definitions of joint configuration, joint and connectionBuilding frames consist of beams and columns, usually made of H or I shapes, that are

assembled together by means of connections. These connections are between two beams, two

columns, a beam and a column or a column and the foundation (Figure 6).

B AA

C

D

A

A

A

D

C

A

D

Figure 6 Different types of connections in a building frame

A connection is defined as the set of the physical components which mechanically fasten the

connected elements. One considers the connection to be concentrated at the location where thefastening action occurs, for instance at the beam end/column interface in a major axis beam-to-

J.1.2.3

J.1.4(7)

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column joint. When the connection as well as the corresponding zone of interaction between the

connected members are considered together, the wordingjointis then used (Figure 7.a).

(a) Single sided joint configuration (b) Double sided joint configuration

Joint

Connection

Right joint

Left joint Rightconnection

Left connection

Figure 7 Joints and connections

Depending on the number of in-plane elements connected together, single-sided and double-

sided joint configurations are defined (Figure 8). In a double-sided configuration (Figure 8.b),

two joints - left and right - have to be considered (Figure 7.b.).

The definitions illustrated in Figure 7 and 8 are valid for other joint configurations and

connection types.

(a) Single-sided (b) Double-sided

Figure 8 In-plane joint configurations

As explained previously, the joints which are traditionally considered as rigid or pinned and aredesigned accordingly, possess, in reality, their own degree of finite flexibility or finite stiffness

resulting from the deformability of all the constitutive components. The next section is aimed at

describing the mainjoint deformability sources.

5. Sources of joint deformability

The rotational behaviour of the joints may affect the local and/or global structural response of

the frames. In this section, the sources of rotational deformability are identified for beam-to-

column joints, splices and column bases.

It is worthwhile mentioning that the rotational stiffness, the joint resistance and the rotation

capacity are likely to be affected by the shear force and/or the axial force acting in the joint.

These shear and axial forces may obviously have contributions to the shear and axialdeformability within the connections. However it is known that these contributions do not affect

significantly the frame response; therefore, the shear and axial responses of the connection, in

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terms of rotational deformability, are neglected.

5.1. Beam-to-column joints

Major axis joints

In a major axis beam-to-column joint, different sources of deformability can be identified. For

the particular case of a single-sided joint (Figure 9.a and 10.a), these are:

The deformation of the connection. This includes the deformation of the connectionelements : column flange, bolts, end-plate or angles,... and the load-introduction deformation

of the column web resulting from the transverse shortening and elongation of the column

web under the compressive and tensile forces Fbacting on the column web. The couple of Fb

forces are statically equivalent to the momentMbat the beam end. These deformations result

in a relative rotation cbetween the beam and column axes; this rotation, which is equal to

b - c (see Figure 9.a) is concentrated mainly along edge AB and provides a flexural

deformability curveMb- c.

The shear deformation of the column web panelassociated with the shear force Vwpacting inthis panel. This leads to a relative rotation between the beam and column axes; this

rotation makes it possible to establish a shear deformability curve Vwp-.

The deformability curve of a connection may obviously be influenced by the axial and shear

forces possibly acting in the connected beam.

Similar definitions apply to double-sided joint configurations (Figure 9.b and Figure 10.b). For

such configurations, two connections and a sheared web panel, forming two joints, must be

considered.

In short, the main sources of deformability which must be contemplated in a beam-to-column

major axis joint are :

Single-sided joint configuration :

- the connection deformabilityMb-ccharacteristic;

- the column web panel shear deformability Vwp-characteristic.Double-sided joint configuration :

- the left hand side connection deformabilityMb1-c1characteristic;

- the right hand side connection deformabilityMb2-c2 characteristic;

- the column web panel shear deformability Vwp-characteristic.

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Mb

Fb

Fb

qb

qc

Mb2

Fb2

Fb2

Mb1

Fb1

Fb1

Fb= Mb/z Fb2= Mb2/z Fb1= Mb1/z

z z

z

A

B

(a) Single-sided joint configuration (b) Double-sided joint configuration

Figure 9 Sources of joint deformability

The deformability of the connection (connection elements + load-introduction) is only due to

the couple of forces transferred by the flanges of the beam (equivalent to the beam end moment

Mb). The shear deformability of the column web panel results from the combined action of these

equal but opposite forces and of the shear forces in the column at the level of the beam flanges.

Equilibrium equations of the web panel provide the shear force Vwp(see Figure 10 for the sign

convention) :

2

V+V-

hM

+M=V

c2c1

b

b2b1n (1)

Another formula to which it is sometimes referred, i.e. :

h

M+M=V

b

b2b1n (2)

is only a rough and conservative approximation of (1).

In both formulae, z is the lever arm of the resultant tensile and compressive forces in the

connection(s). Guidance on the derivation of zis given in the lecture on "Characterisation and

idealisation of moment resisting joints".

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(a) Single-sided joint (b) Double-sided joint

Joint configurations

Vc1

Nc1

Mc1

Vc2

Nc2Mc2

Vb1

Mb1

Vc1

Nc1

Mc1

Vc2

Nc2

Mc2

Vb1

Nb1

Mb1

Vb2

Nb2

Mb2

Web panels

Vwp

zVwp

Vwp

Vwpz

Connections

Vb1

Nb1

Mb1

Vb2

Nb2

Mb2

Vb1

Nb1

Mb1

Nb1

Vb1 Vb1

Figure 10 Loading of the web panel and the connections

Minor axis joints

A similar distinction between the web paneland the connectionshall also be made for a minoraxis joint (Figure 11). The column web exhibits a so-called out-of-plane deformability while the

connection deforms in bending as it does in a major axis joint. However no load-introduction

deformability is involved.

In a double-sided joint configuration, the out-of-plane deformation of the column web depends

on the bending moments experienced by the right and left connections (see Figure 12):

M-M=M b2b1b (3)

For a single-sided joint configuration (Figure 11), the value of Mbequals that ofMb.

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Mb

Fb

Fb

Fb=Mb/Z

Z

Figure 11 Deformability of a minor axis joint

Mb1Mb2

Figure 12 Loading of a double-sided minor axis joint

Joints with beams on both major and minor column axes

A 3-D joint (Figure 13) is characterised by the presence of beams connected to both the column

flange(s) and web. In such joints, a shear deformation and an out-of-plane deformation of the

column web develop coincidently.

The loading of the web panel appears therefore as the superposition of the shear loading given

by formulae (1) or (2) and the out-of-plane loading given by formula (3).

The joint configuration of Figure 13 involves two beams only; configurations with three or four

beams can also be met.

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Mc

Nc

Mc

Nc

Mc

Nc

Mc

Nc

Upper connection

Lower connection

Upper connection

Lower connection

Figure 15 Deformation of a column splice

5.3. Beam-to-beam joints

The deformability of a beam-to-beam joint (Figure 16) is quite similar to the one of a minor axis

beam-to-column joint; the loadings and the sources of deformability are similar to those

expressed earlier for minor axis joints.

Mb

Figure 16 Deformation of a beam-to-beam joint

5.4.Column bases

In a column base, two connection deformabilities need to be distinguished (Figure 17) :

the deformability of the connection between the column and the concrete foundation(column-to-concrete connection);

the deformability of the connection between the concrete foundation and the soil (concrete-to-soil connection).

For the column-to-concrete connection, the bending behaviour is represented by a Mc- curve,

the shape of which is influenced by the ratio of the bending moment to the axial load at the

bottom of the column.

For the connection between the concrete foundation and the soil, two basic deformability curves

are identified:

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aNc-ucurve which corresponds to the soil settlement due to the axial compressive force inthe column; in contrast with the other types of joint, this deformability curve may have a

significant effect on the frame behaviour;

aMc- curve characterising the rotation of the concrete block in the soil.As for all the other joints described above, the deformability of the column base due to the shearforce in the column may be neglected.

The column-to-concrete connection and concrete-to-soil connection Mc- characteristics are

combined in order to derive the rotational stiffness at the bottom of the column and conduct the

frame analysis and design accordingly.

Similar deformability sources exist in column bases subjected to biaxial bending and axial

force. The connectionMc-characteristics are then defined respectively for both the major and

the minor axes.

Column-to-concrete"connection"

Nc

Mc

Concrete-to-soil"connection"

Figure 17 The connections in a column base

6. Joint c lassification

6.1. General

Later in this lecture, it is shown that the joints need to be modelled for the global frame analysis

and that three different types of joint modelling are introduced : simple, semi-continuous and

continuous.It will also been explained that the type of joint modelling to be adopted is dependent both on

the type of frame analysis and on the class of the joint in terms of stiffness and/or strength.

Classification criteria are used to perform this task and these are described below.

6.2. Stiffness classification

The stiffness classification into rigid, semi-rigid and pinned joints is performed by comparing

simply the design joint stiffness to two stiffness boundaries (Figure 18). For sake of simplicity,

the stiffness boundaries have been derived so as to allow a direct comparison with the initial

design joint stiffness, whatever the type of joint idealisation that is used afterwards in the

analysis.

J.2.2.1(1)

J.2.2.2(1)

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Sj,ini

Pinned

Semi-rigid

RigidMj

Boundaries for stiffness

Joint initial stiffness

Figure 18 Stiffness classification boundaries

6.3. Strength classification

The strength classificationsimply consists of comparing the joint designmoment resistance to

"full-strength" and "pinned" boundaries (Figure 19).

Mj,Rd

Partial-strength

Full-strength

Pinned

Mj

Boundaries for strength

Joint strength

Figure 19 Strength classification boundaries

6.4. Boundaries for classification

It is while stressing that a classification based on the experimental joint M-characteristics is

not allowed, asdesignproperties only are of concern.

The stiffness and strength boundaries for the joint classification are given as follows :

Classification by stiffness

rigid joint S j,ini25 EI/L(unbraced frames)

Figure J.8

J.2.2.2

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S j,ini8 EI/L(braced frames)

semi-rigid joint L/EI25SL/EI5,0 ini,j


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rigid/full-strength;

rigid/partial-strength;

pinned.

However, as far as the joint rotational stiffness is considered, joints designed for economy maybe neither rigid nor pinned but semi-rigid. There are thus new possibilities for joint modelling:

semi-rigid/full-strength;

semi-rigid/partial-strength.

With a view to simplification, Eurocode 3 - Chapter 6 and Annex J account for these

possibilities by introducing three joint models (Table 1) :

continuous: covering the rigid/full-strength case only;

semi-continuous: covering the rigid/partial-strength, the semi-rigid/full-strength

and the semi-rigid/partial-strength cases;

simple: covering the pinned case only.

STIFFNESS RESISTANCE

Full-strength Partial-strength Pinned

Rigid Continuous Semi-continuous *

Semi-rigid Semi-continuous Semi-continuous *

Pinned * * Simple

* : Without meaning

Table 1 Types of joint modelling

The following meanings are given to these terms :

continuous: the joint ensures a full rotational continuity between the connectedmembers;

semi-continuous: the joint ensures only a partial rotational continuity between theconnected members;

simple: the joint prevents from any rotational continuity between theconnected members.

The interpretation to be given to these wordings depends on the type of frame analysis to be

performed. In the case of an elastic global frame analysis, only the stiffness properties of the

joint are relevant for the joint modelling. In the case of a rigid-plastic analysis, the main joint

feature is the resistance. In all the other cases, both the stiffness and resistance properties govern

the manner in which the joints should be modelled. These possibilities are illustrated in Table 2.

TYPE OF FRAME ANALYSIS

MODELLING Elastic analysis Rigid-plastic

analysis

Elastic-perfectly plastic

and elastoplastic analysis

Continuous Rigid Full-strength Rigid/full-strength

Semi-continuous Semi-rigid Partial-strength Rigid/partial-strength

Semi-rigid/full-strength

Semi-rigid/partial-strength

Simple Pinned Pinned Pinned

Table 2Joint modelling and frame analysis

7.2. Modelling and sources of joint deformability

J.2.3.2 andJ.2.3.3

Figure J.5

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The difference between the loading of the connection and that of the column web in a beam-to-

column joint requires, from a theoretical point of view, that account be taken separately of both

deformability sources when designing a building frame.

However doing so is only feasible when the frame is analysed by means of a sophisticated

computer program which enables a separate modelling of both deformability sources. For most

available software, the modelling of the joints has to be simplified by concentrating the sources

of deformability into a single rotational spring located at the intersection of the axes of the

connected members.

7.3. Simpli fied modelling according to Eurocode 3

For most applications, the separate modelling of the connection and of the web panel behaviour

is neither useful nor required; therefore only the simplified modelling of the joint behaviour will

be considered in the present document. This idea is the one followed in the ENV 1993-1-1

experimental standard (Chapter 6 and Annex J ). Table 3, taken from the revised Annex J,

shows how to relate the simplified modelling of typical joints to the basic wordings used for the

joint modelling: simple, semi-continuous and continuous.

JOINT

MODELLING

BEAM-TO-COLUMN JOINTS

MAJOR AXIS BENDING

BEAM

SPLICES

COLUMN

BASES

SIMPLE

Table 3 Simpli fied modelling for joints according Eurocode 3

7.4. Concentration of the joint deformability

For normal practice taking account of both the flexural behaviour of the connection and theshear (major axis beam-to-column joint) separately or out-of-plane behaviour of the column

web panel (minor axis beam-to-column joint configurations or beam-to-beam configurations) is

not feasible. This section is aimed at explaining how to concentrate the two deformabilities into

a single flexural spring located at the intersection of the axes of the connected members.

Major axis beam-to-column joint configurations

In a single-sided configuration, only one joint is concerned. The characteristic shear-rotation

deformability curve of the column web panel (Figure 20.b) is first transformed into aMb-curve

through the use of the transformation parameter . This parameter, defined in Figure 21.a,

relates the web panel shear force to the (load-introduction) compressive and tensile forces

connection (see also formulae 1 and 2).

TheMb-spring characteristic which represents the joint behaviour is shown in Figure 20.a; it isobtained by summing the contributions of rotation, from the connection (c) and from the shear

J.2.3.3

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panel (). The Mj-characteristic of the joint rotational spring located at the beam-to-column

interaction is assumed to identify itself to theMb-characteristic obtained as indicated in Figure

20.c.

Mb, Mj

c,i+iMb,i

Mb

Mb,i

Mb

ciMb,i

(a) Connection (b) Shear panel (c) Spring

c

Figure 20 Flexural characteristic of the spring


Vwp= Fb Vwp= 1Fb1 = 2Fb2

where Fb= Mb/z where Fb1= Mb1/z Fb2= Mb2/z

MbFb

Fb

Vwp

Vwp

Mb1Fb1

Fb1

Vwp

Vwp

Mb2Fb2

Fb2

Figure 21 Definit ion of the transformation parameter for major

axis joints

In a double-sided configuration, two joints - the left one and the right one are involved. The

derivation of their corresponding deformability curves is conducted similarly as in a single-

sided configuration by using transformation parameters 1and 2 (Figure 21.b).

Because the values of the parameters can only be determined once the internal forces are

known, their accurate determination requires an iterative process in the global analysis. For

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practical applications, such an iterative process is hardly acceptable provided safe values are

available. These values may be used a priori to model the joints and, on the basis of such joint

modelling, the frame analysis may be performed safely in a non-iterative way.

The recommended but approximate values of , where1 is taken as equal to 2 for double-

sided configurations, are given in the Lecture on "Practical procedures for the characterisation

of the response of moment resisting joints". They vary from = 0 (double-sided joint

configuration with balanced moments in the beams) to= 2(double-sided joint configuration

with equal but unbalanced moments in the beams). These two extreme cases are illustrated in

Figure 22.

(a) Balanced beam moments

MbMb

(b) Equal but unbalanced beam moments

=2

MbMb

=0

Figure 22 Extreme cases for values

Mb= Mb Mb= 1Mb1 = Mb = 2Mb2

= 1


Mb Mb2Mb1

Figure 23 Definit ion of the transformation parameter for minor

axis joints

Minor axis beam-to-column joint configurations and beam-to-beamconfigurations

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Development ofA Trans-national Approach

Course: Eurocode 3

Module 5 : Structural Joints

Lecture 16: Simple JointsSummary:

This lecture is intended to introduce the concept of simple jointsas a limiting condition of all joints.

The requirements relating to stiffness, strength androtation capacityare listed.

Joints are described as an assemblage of componentseach of which may be regarded as a link in achain. The strength of the weakest link controls the overall load carrying capacity of the system.

Examples of simple beam to column and beam to beam joints are given.

Pre-requisites: (what prior knowledge is required of the student?)

A knowledge of structural analysis

Helpful ( but not essential ) to understand plastic response of frames

Lecture on Generalities about Structural Joints

Notes for Tutors:

This material comprises one 30 minute lecture.

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Objectives:The student should:

Understand the conceptual assumption of simple joints. Appreciate the basic reasoning for the approximation

Be able to examine a joint and identify the individual components and force transfers which occur in the

joint.

Know where to look for clauses governing these force transfers.

Be able to assess the capacity of a joint when worked examples have been studied.

References: (essential & background reading)

Owens, G.W. and Cheale, B.D.,Structural Steelwork Connections, Butterworth & Co., Salisbury,

1989. Kirby, P.A.,Bitar, S and Gibbons, C.,The Design of Columns in Non-Sway Semi-Rigidly Connected

Frames,First World Conference on Constructional Steel Design, Acapulco, Mexico, December 1992.

Contents

1. Introduction

1.1 Condition 1 : Strength1.2 Condition 2 : Stiffness

1.3 Condition 3 : Rotation Capacity

2. Types of Joint

2.1 Beam to Column Joints

2.2 Beam to Beam Joints

2.2.1 Primary to Secondary Beams

2.2.2 Beam Splices

3. Concluding Summary

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1. Introduction

Beam-to-column and beam-to-beam joints are traditionally designed as pinned or rigid eventhough the most flexible of these will provide some resistance to moment whilst the stiffest will

have some small degree of flexibility. As was argued in the lecture on Generalities of

Structural Joints, simple joints are presumed to possess no resistance to moment whatever the

rotation at the joint. In a frame which is prevented from swaying, this assumption makes the

structure behave as a collection of statically determinate components which may then be readily

analysed by hand and, equally importantly, each member may be proportioned without

reference to the rest of the structure. If the joints are assumed to be rigid, the frame may be

analysed using a relatively straightforward analysis though the resulting computations are

considerably more complex than for a pin-jointed frame. It can be appreciated that theassumptions regarding the pinned and rigid approximations have arisen because of the resulting

simplifications in frame analysis and hence in the design process. Although computational

capabilities have improved dramatically during the past couple of decades, most frames are still

designed using these assumptions which represent the limiting moment - rotation stiffnesseswhich can exist in joints. This implies that frames designed using the assumption of pinned

joints will not be capitalising on the inherent stiffness possessed by even the simplestconnections whilst fames designed using continuous construction ( rigid joints ) will probably

involve the expense of complex joints often incorporating the use of stiffeners in order to

achieve the requisite stiffness in the joint. In reality, all practical joints have moment - rotation

characteristics which correspond to stiffnesses intermediate between these two extreme cases.

In addition to the consideration of joint stiffness referred to above, there is a second factor

which must be accounted for in joint design, namely strength. By definition, a joint which istruly pinned possesses zero resistance to moment. However, other joints may be either full

strength - if the moment resistance of the joint exceeds that of the connected members - or

partial strength if its resistance is less than that of the connected members. This situation is also

described in lecture 4 : Frame Analysis and Design.

To fully satisfy the definition of a true pinned joint would require the production of an

expensive detail. This is not justifiable as, for many years, designers have been producing

highly successful frames using the assumption, and without such expense. There is a range of

situations for which small stiffness and strength may be neglected. EC3 states that a

nominally pinned connection shall be so designed that it cannot develop significant moments

which might adversely affect members of the structure. Clearly the connection must

nevertheless be capable of successfully transferring the forces arising at the location and mustbe capable of undergoing any required deformations without distress. This implies that, if the

frame is designed plastically, the connection must be able to rotate sufficiently to permit all of

the hinges of the mechanism to develop. This gives rise to the requirement of adequate rotation

capacity. Consideration of a joint assumed to resist zero moment shows that such joints must

also be capable of accepting rotation without losing the ability to resist actions such as shear.

Thus it can be seen that, in general, a connection has three distinct properties

(i) Strength - its moment resistance.

(ii) Stiffness - related to the slope of its moment - rotation relationship.

(iii) Deformability - its rotation capacity.

In order to determine whether or not a connection will satisfy the condition that moments will

not adversely affect the performance of the frame, considerable research has shown that a beam

to column connection may be classified as nominally pinned if the two conditions listed below,are satisfied.

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1.1 Condi tion 1: STIFFNESS

This rotational stiffness Sj must satisfy the condition

Sj,ini0,5 E Ib/ Lb (1)

where Sj,ini is the initial rotational stiffness of the connection.

Ib is the second moment of area of the connected beam.

Lb is the length of the connected beam.

In the ENV version of the Eurocode , in Chapter 6, the relevant stiffness was specified as Sj, ,

which was measured with reference to the point on the moment - rotation characteristic at the

design moment resistance, MRd. However in the revised Annex J this has been replaced by the

initial stiffness, Sj,ini.

RevisedAnnex J

1.2 Condi tion 2 : STRENGTH

The design moment resistance of the joint, MRd, must not exceed 0,25 times the design plasticmoment resistance, Mpl.Rd, of the weaker connected member or members as shown in Figure 1.

Mpc

Mpc

Mpb Mpb

Mpc

Mpc

Mpcis fully plastic moment of resistance of column

Mpbis fully plastic moment of resistance of beam

Figure 1 Maximum moment resistance requirement for s imple join ts.

If Mpb< 2Mpc

then Mj,Rd = 0,25Mpb

If Mpb> 2Mpc

then Mj,Rd= 0,25x2xMpc

In addition to satisfying the above requirements for a joint detail to be considered to be a

pinned connection, the designer must ensure that the shear ( the end reaction of the beam ) and

any axial force can be safely transferred between the connected members. The principal actionto be considered is the transferrence of the reaction from the end of the beam through to the

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supporting member. This reaction may also be accompanied by a tying force and it may be

necessary to combine these two actions to determine their resultant.

1.3 Condi tion 3 : ROTATION CAPACITY

A further consideration which is included relates to the ability of the joint to remain coherent

and accept imposed rotations without rupture ( for example welds must not fracture ) before

sufficient rotations have occurred which allow the full loading to be carried, nor should the

joint acquire an undesirable stiffness during the development of the required rotations.

Considering first the problem of the development of an undesirable stiffness. The most obvious

situation which might give rise to such an effect is the closure of a gap which causes two

surfaces to come into bearing. This might lead to an increased stiffness which is inappropriate

for simple design, as indicated in Figure 2. Calculations on a medium sized beam ( about 450

mm deep ) and spanning 6.0m shows that the rotations resulting from the application of amaximum factored loading causes a gap of some 10mm to be produced at one extremity of the

beam end, if the rotational end restraint is truly zero. Of course the size of this gap willincrease with beam depth. In practice there will always be some resistance to rotation and this

will reduce the size of the gap required and the actual span moment which will arise at the

midspan of the beam. Thus the assumption of zero restraint is safe for beams. The effect on

columns is, at first sight, somewhat different as any moment attracted to the joint will be

transferred to the column. However extensive studies, both theoretical and experimental, have

demonstrated that the effect of any adverse moment transferred from the beam to the column

because of the stiffness of the joint is offset by the restraint provided to the column by the beam

due to the stiffness of the joint. Further information on this phenomenon may be found in the

second of the references.

Figure 2 Effect of gap closure.

M

Contact betweenbeam flange andcolumn face.

M

The other phenomenon which must be considered is the mode of failure within a joint. For

cleated connections, the problems associated with overstrength material is covered in revised

Annex J where hidden factors have been included in the formulations which cater for the

possibility of this effect. They ensure that failure is in the angle sections and does not occur in

the bolts thus ensuring that a ductile ( rather than a brittle ) failure occurs which, in general,

leads to an adequate rotation capacity.

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2. Types of Joint.

The most common joints which are used for simple connections between beams and columnsare seat and web cleats, top and seat cleats,web cleats, flexible end plate connections and shear

plates. Figure 3 shows a number of typical details of such arrangements. Variations on these

arrangements are often used for connections between primary and secondary beams and Figure

4 shows two possible examples. The choice of the specific joint type to be adopted will usually

be controlled by the type of equipment possessed by the fabricator, but will also be influenced

by experience gained from past practice and by the requirements relating to the erection process

on site. This last mentioned consideration will often lead to the removal of parts of the beam

section, as can be seen from Figure 4 for the beam-to-beam connections. Similarly parts of thebeam are often removed for beam to column joints to facilitate the erection process.

At every stage of load transfer safety must by assured by adequate capacitywith due regard for

sufficient flexibility and rotation capacity. The latter conditions are generally assessed by

experience rather than specific calculation but the first requires specific compliance with

codified conditions.

As can readily seen from the above, a joint consists of a number of components which togethereffect the connection of the members, and a whole series of load transfers are involved. The

total effect may be likened to links in a chain and, if any one of the links is not adequate, the

chain will break and the joint will fail. The principal transfers are usually made by welding and

/or bolting although rivetting is occassionally used. Generally the fabrication is arranged such

that the connection of elements which is undertaken in the fabrication shop is by welding,

whilst that performed on site is by bolting. However such advice is by way of a generalisationrather than a specific requirement but does reflect the current trend which is largely governed

by economics.

2.1 Beam to Column Joints

Considering the simple web angle connection shown in Figure 5, it can be appreciated that the

angle sections may be bolted to both the column face and the beam web and no welding is

involved. Alternatively the angles may be welded either to the column face, or to the beam

web, in the workshop with the other fastening be made by bolting on site. A number of checks

are needed to demonstrate the adequacy of the connection shown. These are listed below.

1)Transfer of the force from the web of the beam into the bolts ( part 1 ). This will involve

consideration of the possibility of block shear failure. The potential failure zone is defined in

Clause 6.5.2.2 and is illustrated in Figure 6.

2)Transfer of the force from the web of the beam into the bolts ( part 2 ). Bearing failure

between the bolts and the beam web. This is defined in Clause 6.5.5. and Table 6.5.3.

3) Shear failureof the bolts connected to the beam web. This aspect is covered in the Clause

6.5.5 and Table 6.5.3 referred to above.

4)Bearing and block shear failurein the outstanding legs of the angle cleats themselves. The

conditions are essentially the same as those in 1) and 2) above.

5)Shear failurein the bolts connected to the column flange. This is as in 3) above.

6)Bearing failurebetween the bolts and the column flange. This is as in 2) above.

Cl 6.5.2.2

Cl 6.5.2.2

Cl 6.5.5

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Double web cleats (minor axiswelded tobeam, bolted tocolumn)

Tab plate: (major axis: weldedto beam, bolted to column)

Seat and stability cleats

(major and minor axes)Top and seat cleats

(major and minor axes)

Shear plate (major axis) Shear plate (major axis)

Single web cleat (major axis:bolted to beam and column)

Welded fin plate: (minor axis:bolted to beam, welded tocolumn)

Figure 3 Common forms of simple joints

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Supporting beam

Supported beam

Supporting beamSupported beam

Single notched angle connection

Double notched end plate connection

Figure 4 Beam to beam connections.

Should any tying forces need to be considered ( as is the case in the U.K. NAD ) then the

connection must also be checked for such action which will involve consideration of the

following potential failure modes, remembering that it will often be necessary to combine the

axial and the shear forces to obtain a resultant action.

Figure 5 Simple web angle connection.

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a1

Lv

a3

a2

Figure 6 Effective area for b lock shear.

1)Block shear failurein the beam web as above but with an amended failure zone.

2)Bearing failurebetween the beam web and the bolts.

3)Shear failureof the bolts.

4)Tensile capacityof the web cleats.

5)Tensile capacityof the bolts to the face of the column.

See Annex Jfor the designrules for suchelements intension

Most of these checks are similar to those made under the action of the vertical reaction force

alone, but others are different. However it can readily be seen that the process is again akin to

confirming that every link in a chain is capable of resisting the applied action and noting that

the strength of the chain is that of its weakest link.

In addition to the above there is a number of requirements relating to the positioning of holes

for bolts which should be satisfied to ensure that there are no unexpected sources of poor

performance ( both in terms of resistance and serviceabilty ) resulting from the detailing. These

conditions also apply to holes for rivets although the use of rivetting is now very limited.

These are covered in Clause 6.5.1 and are summarised below.

Cl 6.5.1

1)Minimum end distance. This should not be less than 1,2 times the diameter of the hole.

2)Minimum edge distance. This should not normally be less than 1,5 times the hole diameter.

3)Maximum end and edge distances. The maximum value should not exceed 40mm plus 4

times the thickness of the thinner part connected when the connection is exposed to the weatheror other corrosive environments. In other circumstances the maximum value should not exceed

150mm or 12 times the thickness of the thinner connected part.

4)Minimum spacing. The spacing between the centres of fasteners in the direction of load

transfer should not exceed 2,2 times the hole diameter but this value may be increased if needed

to provide adequate bearing resistance.

5)Maximum spacing. Certain requirements exist which relate to joints in tension and

compression members and these are rarely appropriate in beam to column connections.

Clearly, for other types of simple joints, the same methodology of decomposing the complex

arrangement of joint components in simple load tranfers will apply, even though the specific

actions checked may differ; for example, no reference has been made to the checking of welds.

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2.2 Beam to Beam Joints

The most common beam to beam joints transfer loading from secondary beams to primary

beams and Figure 4 shows two typical details which might be used for this purpose. The first is

an example where the primary (supporting) beam is deeper than the secondary (supported)beam, whilst the second illustrates a solution where both primary and secondary beams are of

equal depth. It is common that the upper surfaces of the beams are desired to be at the same

elevation and these two examples meet this requirement, but this is not always the case.

A second form is a splice within a beam length. The basic actions involved in beam to beam

joints are structurally similar to those in beam to column joints and will not be repeated here.

2.2.1 Beam to Beam Joints: Primary to Secondary BeamsThe major differences occur as a result of the differing detailing arrangements which arise

largely as a result of construction requirements. Figure 4(b) shows a joint at the end of a

secondary beam which frames into a primary beam. The thin end plate is welded to the end of

the secondary beam ( possibly with limited depth ) and the joint is completed by bolting the

end-plate to the web of the primary beam. This is a popular detail mimising site work. It doeshowever suffer from the fact that it may be difficult to slew the beam into place and, in

addition, there is no adjustment for overlength secondary beams. It may be desirable to cut the

beams undersize and, with the beam in position, make up the length with packing plates which

may be slid in with the secondary beam in place.

An alternative to the use of an end plate involves the use of one or a pair of angles as indicated

in Figure 4(a). Bolted connections are made to the webs of the primary and secondary beams

by these web cleats which have the advantage that adjustments for small discrepances in length

andalignment can be accommodated by clearance in the holes in the beam webs and the angle

sections. Extra allowance can be made through the use of slotted holes.

Both of these arrangements however, will lead to the upper flanges of the primary and

secondary beams not being at the same level if the beam centrelines are at the same elevation.

The examples of Figure 4 place the upper surfaces at the same elevation but this has requiredthat the secondary beam flanges have been cut away to facilitate the construction even in the

case where the depth of the secondary beam would otherwise allow it to pass between the

flanges of the primary beam.. This cutting away process is known as coping.This introduces a new factor which must be considered in assessing the design strength of the

joint; namely a revision to the shear block, as it must be recognised that the I beam has been

reduced to an inverted T section. There is also a consequent loss of in-plane, out-of-plane and

torsional strength and stiffness in the coped region and consideration should be given to localbuckling of the unrestrained portion of the web of the coped beam. Sometimes it may be

desirable to provide local stiffening.

2.2.2 Beam to Beam Joints: Beam SplicesBeam splices occur where a construction joint is placed in a beam member. Usually this is inthe form of a moment resisting joint designed to create a beam of the same cross-sectional

properties ( for example flexural rigidity and moment resistance ) as those of the component

beams when the total length is excessive for transportation or construction.. Such a joint would

be designed as a rigid, full strength joint and is outside the scope of this lecture, but there may

be occasions when articulation is required. Under these circumstances the principles developed

in this presentation should be followed.

Occasionally it may be desirable to make a simple connection if, for example, the joint is made

at a point which is the moment is required to be zero; it could be that it is desired to restrict thesagging moment in the one part of the beam by ensuring that no moment is transferred at the

joint. However, this condition of zero moment is unlikely to be fully realised in practice.

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It can be seen that these joints may be considered in a fashion similar to that described for beam

to column joints in that equivalent individual checks ensure that the complete load path is

sufficiently strong so that the load transfer may be accomplished. In addition, flexibility and

rotation capacity considerations must receive proper attention, and sufficient clearances must beprovided to ensure that, during the anticipated rotations, no surfaces come into contact which

would drammatically increase the stiffness to an undesirable level.

3. Concluding Summary

This lecture has introduced the philosophy of simple joints both in respect of idealised

behaviour and real response.

The concept of a joint as an assemblage of components which act as a number of links in a

chain has been introduced.

The requirements of strength, stiffness and rotation capacity have been outlined - as have the

code requirements.

Examples of practical details for beam to column and beam to beam joints have been given.

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Development ofA Trans-national Approach

Course: Eurocode 3

Module 5 : Structural joints

Lecture 17 : Characterisation and idealisation ofmoment resisting joints

Summary:

The principles of the component method for joint characterisation are presented and, in a specificannex, the bases of the so-called assembly procedure, which is one of the three steps of the component

method, are described.

The idealisation of the moment-rotation characteristic of the joints is introduced : it consists in selectingthe shape of the moment-rotation relationship which is the most appropriate to the type of global frame

analysis which is planned (elastic, rigid-plastic, ).

Pre-requisites:

Basic knowledge on frame analysis and design

Basic definitions and concepts on semi-rigid joints

Notes for Tutors:

This material comprises one 30 minutes lecture (70 minutes with the annex)

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Characterisation and idealisation of moment resisting joints

Objectives:

The student should:

Know, at least physically, how to characterise and idealise the response of a structural joint in view of a

global frame analysis

References:

Revised Annex J of Eurocode 3, "Joints in Building Frames", Amendment 2 to ENV 1993-1-1, 1998

Frame design including joint behaviour. Users manual published by the European Union, Report EUR18563 EN, Office for Official Publications, Luxembourg, 1998 (ISBN 92-828-4904-X)

Contents:

1. Joint characterisation

1.1. General1.2. Introduction to the component method

2. Joint idealisation

Annex A Evaluation of the stiffness and resistance properties of the joints according to Eurocode 3-

(revised) Annex J

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1. Joint characterisation

1.1. GeneralAn important step when designing a frame consists of the characterisation of the rotational

response of the joints, i.e. the evaluation of the mechanical properties in terms of stiffness,

strength and ductility.

Three main approaches may be followed :

experimental

numerical

analytical.The only practical option for the designer is the analytical approach. Analytical procedures have

been developed which enable a prediction of the joint response based on the knowledge of the

mechanical and geometrical properties of the joint components.In this section a general analytical procedure, termed component method, is introduced. It

applies to any type of steel or composite joints, whatever the geometrical configuration, the type

of loading (axial force and/or bending moment, ...) and the type of member sections.

The method is used in the Lecture on Practical procedures for the characterisation of the

response of moment resisting joints where the mechanical properties of joints subjected to

bending moment and shear force are computed.

1.2. Introduction to the component method

The component method considers any joint as a set of individual basic components. For the

particular joint shown in Figure 2.b. (joint with an extended end-plate connection subject to

bending), the relevant components are the following :

Compression in zone :

column web in compression;

beam flange and web in compression;

Tension zone :

column web in tension;

column flange in bending;

bolts in tension;

end-plate in bending;

beam web in tension;

Shear zone :

column web panel in shear.

Each of these basic components possesses its own strength and stiffness either in tension or in

compression or in shear. The column web is subject to coincident compression, tension and

shear. This coexistence of several components within the same joint element can obviously lead

to stress interactions that are likely to decrease the resistance of the individual basic

components.

The application of the component method requires the following steps :

a) identification of the active components in the joint being considered;

b) evaluation of the stiffness and/or resistance characteristics for each individual basic

component (specific characteristics - initial stiffness, design resistance, ... - or the wholedeformability curve) ;

J.1.5

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c) assemblyof all the constituent components and evaluation of the stiffness and/or resistance

characteristics of the whole joint (specific characteristics - initial stiffness, design resistance,

... - or the whole deformability curve).

In Figure 1, the principles of the component method are illustrated in the specific case of a

beam-to-column joint with a welded connection.

COMPONENT METHOD

Three steps

First step:

Identification of thecomponents

Second step:Response of the

components

Third step:

Assembly of the

components

Column web Column web Column web

in shear in compression in tension

Stiffness coefficient ki of each component

Resistance FRdiof each component

Stiffness of the joint Sj,ini= Ez/kiResistance of the joint MRd= min(FRdi).z

F

F

M=Fz

F

1

FRd1Ek1

F

1

FRd2Ek2

F

1

FRd3Ek3

M

MRd

Sj,ini

Figure 1 Application of the component method to a welded joint

The assembly procedure consists in deriving the mechanical properties of the whole joint from

those of all the individual constituent components. This requires a preliminary distribution of

the forces acting on the joint into internal forces acting on the components in a way that satisfies

equilibrium.

In Eurocode 3 Annex J,the analytical assembly procedures are described for the evaluation of

the initial stiffness and the design moment resistance of the joint. These two properties enable

the designer to determine the design joint moment-rotation characteristic whatever the type of

analysis (Figures 4 to Figure 6). In Annex A of the present lecture, information is provided onhow the stiffness and strength assembly is carried out.

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The application of the component method requires a sufficient knowledge of the behaviour of

the basic components. Those covered by Eurocode 3are listed in Table 1. The combination of

these components allows one to cover a wide range of joint configurations, which should be

sufficient to satisfy the needs of practitioners as far as beam-to-column joints and beam splices

in bending are concerned. Examples of such joints are given in Figure 2.

Some fields of application can also be contemplated :

Joints subject to bending moment (and shear) and axial force;

Column bases subject to coincident bending moment, shear force and axial force where thecomponents such as :

- concrete foundation in compression;

- end-plates with specific geometries;

- anchorages in tension;

- contact between soil and foundation,

will be activated.

These situations are however not yet covered, or only partially covered, byEurocode 3.

Table J.1

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NComponent

1Column web panel in shear

VSd

VSd

2 Column web in compression

Fc.Sd

3 Beam flange and web in compression

Fc.Sd

4 Column flange in bending

Ft.Sd

5 Column web in tension

Ft.Sd

6 End-plate in bending Ft.Sd

7 Beam web in tension Ft.Sd

8 Flange cleat in bending Ft.Sd

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9 Bolts in tension Ft.Sd

10 Bolts in shear Fv.Sd

11 Bolts in bearing (on beam flange,

column flange, end-plate or cleat)

Fb.Sd

12 Plate in tension or compression Ft.Sd

Fc.Sd

Table 1 List of components covered by Eurocode 3

Figure J.4

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(a) Welded joint (b) Bolted joint with extended end-plate

(c) Two joints with flush end-plates (d) Joint with flush end-plate(Double-sided configuration)

(e) End-plate type beam splice (f) Cover-joint type beam splice

(g) Bolted joint with angle flange cleats (h) Two beam-to-beam joints (Double-sided configuration)

Figure 2 Examples of joints coveredby Eurocode 3

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2. Joint idealisation

The non-linear behaviour of the isolated flexural spring which characterises the actual jointresponse does not lend itself towards everyday design practice. However the moment-rotation

characteristic curve may be idealised without significant loss of accuracy. One of the most

simple idealisations possible is the elastic-perfectly plastic relationship (Figure 3.a). This

modelling has the advantage of being quite similar to that used traditionally for the modelling of

member cross-sections subject to bending (Figure 3.b).

The momentMj,Rdthat corresponds to the yield plateau is termed the designmoment resistance

in Eurocode 3. It may be considered as the pseudo-plastic moment resistance of the

joint. Strain-hardening effects and possible membrane effects are henceforth neglected, which

explains the difference in Figure 3 between the actualM- characteristic and theyield plateau

of the idealisation.

S ,ini/

Mj

Mj,Rd

EI/L

Mb, Mc

Mpl,Rd

Actual M-characteristic Idealised M-characteristic

(a) Joint (b) Member

Figure 3 Bi-linearisation of moment-rotation curves

The value of the constant stiffness Sj.ini/is discussed below.

In fact there are different possible ways to idealise a jointM-characteristic. The choice of one

of them is dependent upon the type of frame analysis which is contemplated:

- Elastic idealisation for an elastic analysis(Figure 4) :

The principal joint characteristic is the constant rotational stiffness.

J.2.1.2

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Sj,ini/

Mj

Mj,Rd

Mj

Mj,Rd

2/3 Mj,Rd

Sj,ini

(a) For elastic verification (b) For plastic verification

Actual M-curve

Idealised representation

Figure 4 Linear representation of a M- curve

Two possibilities are offered inEurocode 3-(revised) Annex J:

Elastic verification of the joint resistance(Figure 4.a) : the constant stiffness is taken equalto the initial stiffness Sj.ini; at the end of the frame analysis, a check that the design moment

MSd experienced by the joint is less than the maximum elastic joint moment resistance

defined as 2/3Mj,Rd.

Plastic verification of the joint resistance(Figure 4.b) : the constant stiffness is taken equalto a fictitious stiffness, the value of which is intermediate between the initial stiffness and

the secant stiffness relative toMj,Rd; it is defined as Sj.ini/. This idealisation is valid for MSd

values less than or equal toMj,Rd. The values of are as follows (Table 2) :

Table 2Values of

- Rigid-plastic idealisation for a rigid-plastic analysis(Figure 5).

Only the design resistanceMj,Rdis needed. In order to allow the possible plastic hinges

to form and rotate at the joint locations, it is necessary to check that the joint has a

sufficient rotation capacity.

J.2.1.3

Type of connection Beam-to-column joint Other types of joint

Welded 2 3

Bolted end-plate 2 3

Bolted cleat 2 3,5

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Mj

Mj,Rd

Figure 5 Rigid-plastic representation of a M- curve- Non-linear idealisation for an elastic-plastic analysis(Figure 6).

The stiffness and resistance properties are of equal importance in this case. The

possible idealisations range from bi-linear or tri-linear representations to the fully non-

linear curve. Again rotation capacity is required in joints where plastic hinges are

likely to form and rotate.

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(a) Bi-linear (b) Tri-linear

Sj,ini/

Mj

Mj,Rd

Mj

Mj,Rd

Mj

Mj,Rd

(c) Nonlinear

Figure 6 Non-linear representations of a M- curve

Annex A Evaluation of the stiffness and resistance

properties of the joints according to Eurocode

3-(revised) Annex J

The component method presented in this lecture is a three step procedure for evaluating thestiffness and resistance properties of structural joints. In the first step, the list of constitutive

components is established. The stiffness and/or resistance properties of the components are then

derived.

The assembly of the components constitutes the third and last step of the method. As its name

indicates, it consists in assembling the individual components so as to derive the mechanical

properties of the whole joint. The relationship between component properties and joint

properties is based on what is commonly called the "distribution of internal forces in the joint".

The latter consists of determining, for a given set of external forces acting on the joint, the

manner in which these forces are distributed between all the constitutive components. The force

to which any given component is subjected is termed the "internal force".

This notion applies not only to structural joints but also to any cross-section in a member and aparallel between these situations is now drawn. In any cross-section of beams and columns, the

6.1.4

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distribution of internal forces in it is required so as to permit computation of its flexural rigidity

or its resistance in bending, shear, torsion and/or axial compression or tension. That is why, in

the following paragraphs, the word "cross-section" covers beam and column sections as much as

joint sections.

The distribution of internal forces has to be carried out in a rational way, and has, from a

theoretical point of view, to fulfil the following requirements :

the internal forces given by the distribution have to be in equilibrium with the externalforces acting on the cross-section;

the compatibility of the displacements between the constitutive parts of the cross-section -namely components in the case of a joint has to be satisfied;

each part of the cross-section has to be able to transfer the internal force to which it issubjected;

the maximum deformation capacity of each part of the cross-section must not be exceeded.In the case of a beam or column H or I cross-section subjected to a bending moment, the

distribution of internal forces - read stresses in this particular case - in the elastic range is

generally assumed to follow the Navier rule (Figure A.1).

Hy

M

=M y

I

.

(a) Beam (b) Internal stresses (c) External force

Figure A.1 Elastic distribution of internal forces (here stresses) in a

beam profi le in bending (I = second moment of area)

fy

m

Figure A.2 Internal forces here stresses corresponding to the

maximum elastic design moment resistance of the cross-section

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fy

m

Figure A.3 Internal forces - stresses here corresponding to the

plastic moment resistance of the cross-section

When the maximum internal stresses (at y = H/2) reach the value of the yield stress fyof theconstitutive steel divided by a partial safety factor M, the maximum elastic moment resistance

of the cross-section is obtained (Figure A.2). The design moment resistance is expressed as :

My

M

y

Rd /Wff

2/H

IM

== (A.1)

where Wis the elastic modulus of the cross-section in bending.

To profit from the extra resistance provided by the plastification of the cross-section, reference

has therefore to be made to the distribution represented at Figure A.3. The design resistance

then becomes :

MyRd /ZfM = (A.2)

whereZdenotes the plastic modulus of the cross-section in bending.

In these distributions, Bernoullis assumption has been considered so as to ensure a

compatibility between the elongation - or shortening - of all the constitutive fibers of the cross-

section. Both elastic and plastic distributions illustrated in Figure A.2 and Figure A.3 are in

equilibrium with the applied external forces and respect the plasticity criterion (fy/M).

Therefore, they satisfy the first three of the four above-mentioned criteria which any distribution

of internal forces should fulfil.

To reach the elastic or plastic moment resistance, the constitutive fibers of the section have to

possess a sufficient deformation capacity so as to reach the yield stress in the case of the elastic

distribution, or, in the case of the plastic distribution, to reach the yield stress and also to allow

a plastic redistribution of the stresses between the adjacent fibers. This means that no prematurelocal buckling of one of the section walls in compression and that no rupture of the material in

tension must occur which would limit the moment capacity of the section. Specific criteria are

provided in the codes so as to prevent the user from overestimating the resistance when such

limitations apply. In these conditions, the fourth criterion on ductility is also fulfilled.

In a H or I profile, it is also common practice to replace the bending moment applied to the

cross-section by a couple of forces located at the level of the centre lines of the beam flanges.

The intensity of the forces is limited to the design resistance of the flanges in tension and

compression, due attention being paid to the possible local buckling of the flange in

compression. The web, the bending resistance of which is neglected, is usually devoted to the

transfer of shear forces. Three of the four identified criteria are therefore satisfied. However the

fourth condition (compatibility) is neglected. This so-called static approach is known to lead to

a safe estimation of the design resistance of the section and is usually followed for sake ofsimplicity.

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The procedure to distribute internal forces within structural joints is quite similar to that

described in the foregoing paragraphs for beam and column cross-sections. In the next

paragraphs, the procedure followed by Eurocode 3-(revised)Annex Jis described; it applies to

steel beam-to-column joints and beam splices where the beam(s) is (are) subject to bending

moments and shear forces. For sake of simplicity and to allow for a hand calculation, two

separate distribution procedures are detailed, one for the evaluation of the elastic initial stiffness

and the other for the assessment of the design resistance of the joint.

The initial elastic stiffness and the design resistance are considered by Eurocode 3as the two

main parameters characterizing the response of a joint in bending. Based on these two values, a

fullM-curve can then be derived as shown in Figure A.4.

Provided that the non-linear M-curve of (revised)-Annex J is not limited by the rotational

capacity (Cd), this curve consists of three parts. Up to a level of 2/3 of the design moment

resistanceMRd, the curve is assumed to be linear elastic and the corresponding stiffness is the

so-called initial stiffness Sj,ini. Between 2/3 MRd and MRd, the curve is non-linear. Once themoment in the joint reachesMRd, a yield plateau develops under further imposed rotations of the

joint.

Figure A.4 Non-

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Joints in Steel construction